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Integral Equation Formulation (integral + equation_formulation)

Distribution by Scientific Domains
Engineering60%

Selected Abstracts

An integral equation solution for three-dimensional heat extraction from planar fracture in hot dry rock

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 12 2003
A. Ghassemi
Abstract In the numerical simulation of heat extraction by circulating water in a fracture embedded in geothermal reservoir, the heat conduction in the reservoir is typically assumed to be one-dimensional and perpendicular to the fracture in order to avoid the discretization of the three-dimensional reservoir geometry. In this paper we demonstrate that by utilizing the integral equation formulation with a Green's function, the three-dimensional heat flow in the reservoir can be modelled without the need of discretizing the reservoir. Numerical results show that the three-dimensional heat conduction effect can significantly alter the prediction of heat extraction temperature and the reservoir life as compared to its one-dimensional simplification. Copyright © 2003 John Wiley & Sons, Ltd. [source]

An efficient method for solving the nonuniqueness problem in acoustic scattering

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2006
A. Mohsen
Abstract The problem of acoustic wave scattering by closed objects via second kind integral equations, is considered. Based on, combined Helmholtz integral equation formulation (CHIEF) method, an efficient method for choosing and utilizing interior field relations is suggested for solving the non- uniqueness problem at the characteristic frequencies. The implementation of the algorithm fully utilizes previous computation and thus significantly reduces the CPU time compared to the usual least-squares treatment. The method is tested for acoustic wave scattering by both acoustically hard and soft spheres. Accurate results compared to the known exact solutions are obtained. Copyright © 2006 John Wiley & Sons, Ltd. [source]

Integral equation methods for scattering by infinite rough surfaces

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2003
Bo Zhang
Abstract In this paper, we consider the Dirichlet and impedance boundary value problems for the Helmholtz equation in a non-locally perturbed half-plane. These boundary value problems arise in a study of time-harmonic acoustic scattering of an incident field by a sound-soft, infinite rough surface where the total field vanishes (the Dirichlet problem) or by an infinite, impedance rough surface where the total field satisfies a homogeneous impedance condition (the impedance problem). We propose a new boundary integral equation formulation for the Dirichlet problem, utilizing a combined double- and single-layer potential and a Dirichlet half-plane Green's function. For the impedance problem we propose two boundary integral equation formulations, both using a half-plane impedance Green's function, the first derived from Green's representation theorem, and the second arising from seeking the solution as a single-layer potential. We show that all the integral equations proposed are uniquely solvable in the space of bounded and continuous functions for all wavenumbers. As an important corollary we prove that, for a variety of incident fields including an incident plane wave, the impedance boundary value problem for the scattered field has a unique solution under certain constraints on the boundary impedance. Copyright © 2003 John Wiley & Sons, Ltd. [source]

Existence of solution in elastic wave scattering by unbounded rough surfaces

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 6 2002
T. Arens
We consider the two-dimensional problem of the scattering of a time-harmonic wave, propagating in an homogeneous, isotropic elastic medium, by a rough surface on which the displacement is assumed to vanish. This surface is assumed to be given as the graph of a function ,,C1,1(,). Following up on earlier work establishing uniqueness of solution to this problem, existence of solution is studied via the boundary integral equation method. This requires a novel approach to the study of solvability of integral equations on the real line. The paper establishes the existence of a unique solution to the boundary integral equation formulation in the space of bounded and continuous functions as well as in all Lp spaces, p,[1, ,] and hence existence of solution to the elastic wave scattering problem. Copyright © 2002 John Wiley & Sons, Ltd. [source]

Sparse solution of an integral equation formulation of scattering from open PEC targets

MICROWAVE AND OPTICAL TECHNOLOGY LETTERS, Issue 3 2006
A. Zhu
Abstract A recently developed compression and sparse solution strategy for electromagnetic problems is applied to integral-equation formulations of scattering from perfectly conducting targets in three dimensions. It is shown that the resulting representations of both the impedance matrix and its inverse are sparse at low-to-moderate frequencies. Limitations and possible extensions of the sparse algorithms are also discussed. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 476,480, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21383 [source]